I just started on factoring with Algebra II. I have been trying to think of something I can do towards the end of the unit to help review the idea of looking at the trinomial to determine which method to use. Is it actually a perfect square? Is it a difference of squares? Is it a perfect cube.
First of all, the I love Math site has three nice games for students to practice factoring trinomials. The first is a factoring puzzle. The students cut the pieces out and then put the pieces together so the original problem and its factored forms lay next to each other. With either problems or factored forms on all four sides of most pieces, the students will have to make sure everything is lined up.
Second is I have, you have a game sort of like fish where students are dealt either the "I have" (the problem) or the "you have" (the factored form). So one person states I have this do you have the factored form ie (x-2)(x+2) for x^2 -4.
Third is Algebra Connect Factoring Game in which students roll a pair of dice to determine which square on the playing board they have to factor. The file comes with everything needed to play this game.
So, why not use a pair of dice to help set the coefficient for the second term and the constant of the trinomial. This means students could end up with zero or negative numbers should you use colored dice. For instance the red die might be negative and the blue positive or you could say in this round all numbers are negative or positive to add a chance for students to obtain different signs.
If students roll a pair of dice twice to get two numbers such as 24 and 11. The problem they have to factor could be x^2 + 11 x + 24 which is (x + 3)(x + 8). On the other hand if they ended up with x^2 + 2x -10, they might not be able to easily factor it and would use the quadratic formula to solve it.
I wanted a game that required the student to think about using the quadratic formula if it can't easily be factored. I admit, I often use the quadratic formula myself because I find it easier with problems that have a leading coefficient.
So I got the idea of using dice to figure out the coefficients for the second term and the constant. Start with a trinomial with a leading coefficent of 1. The students roll two dice to determine what the coefficient of the middle term. They roll the two dice for the constant. This gives them possibilities of 11 to 66 and a variety of numbers in between.
The nice thing is that using dice means the numbers change with a certain amount of randomness and the game can easily be replayed as needed.